Question

Simplify the following:-

$\tt\orange{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{4}{3}÷\frac{4}{12} }}$​

Answer 1

Step-by-step explanation:

$\tt\red{Hey\:Mate}$

$\tt\blue{Here\:is\:ur\: answer}$

$\fbox{Important\: concepts}$••

a). $\bf\green{\underline{BODMAS}}$::

BODMAS is the application used for simplifying the mathematical problems by using the sequence of BRACKET,OF,DIVISION, MULTIPLICATION, ADDITION and SUBTRACTION.

b). $\bf\green{\underline{RECIPROCAL}}$::

RECIPROCAL is the reverse of a fraction or a number. Reverse can be obtained by multiplying $\frac{1}{number}$ to the number.

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$\bf\pink{\underline{Given}}$::

$\tt\orange{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{4}{3}÷\frac{4}{12} }}$

${\boxed \tt\red{Apply \:the\: BODMAS\:rule}}$

$\fbox{BODMAS}$::

$\bf\red{B}$ = Bracket

$\bf\red{O}$ = Of

$\bf\red{D}$ = Division

$\bf\red{M}$ = Multiplication

$\bf\red{A}$ = Addition

$\bf\red{S}$ = Subtraction

Here, there are no brackets and of.

So, here we will apply DMAS rule.

$\tt\blue{DMAS}$::

$\bf\red{D}$ = Division

$\bf\red{M}$ = Multiplication

$\bf\red{A}$ = Addition

$\bf\red{S}$ = Subtraction

First we will do division then multiplication and then addition and subtraction respectively.

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{4}{3}÷\frac{4}{12} }}$

The fraction after divide sign will get reversed.

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{4}{3}\times \frac{12}{4} }}$

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{12}{12} }}$

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{1}{1} }}$

Here, 1 can be excluded as it returns dame value after adding and subtracting.

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4} }}$

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times 4}}$

$\tt\blue{\implies}{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+3 }}$

Now, we will take the $\tt\red{LCM}$.

LCM of 3,6 and 8 by taking common multiples.

Multiples of 3: 3 6 9 12 15 18 21 $\fbox{8}$

Multiples of 6: 6 12 18 $\fbox{24}$

Multiples of 8: 8 16 $\fbox{24}$

So, the LCM is $\tt\red{24}$.

Now we will make $\fbox{EQUIVALENT\: FRACTION}$.

$\tt\purple {\frac{2}{3}= \frac{2\times 8}{3 \times 8} \implies \frac{16}{24}}$

$\frac{5}{6}= \frac{5 \times 4}{6 \times 4}\implies \frac{20}{24}$

$\frac{7}{8}= \frac{7 \times 3}{8 \times 3}\implies \frac{21}{24}$

$\frac{3}{1}= \frac{3 \times 24}{1 \times 24}\implies \frac{72}{24}$

$\tt\blue{\implies}{\boxed{\frac{16}{24}+\frac{20}{24}-\frac{21}{24}+\frac{72}{24} }}$

$\tt\blue{\implies}{\boxed{\frac{16+20-21+72}{24}}}$

$\tt\blue{\implies}{\boxed{\frac{108-21}{24}}}$

$\tt\blue{\implies}{\boxed{\frac{87}{24}}}$

$\tt\green{\longmapsto}{\boxed{\frac{87}{24}}}$

Thus , answer of following question is $\mathfrak\red{\frac{87}{24}}$

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Answer 2

Step-by-step explanation:

$\tt\orange{\boxed{\frac{2}{3}+\frac{5}{6}-\frac{7}{8}+\frac{3}{4}\times\frac{4}{3}÷\frac{4}{12} }}$

By BODMAS

2/3+5/6-7/8+3/4×4/3×12/4

=2/3+5/6-7/8+3/4